Rashida Jones plays the title character - a feisty, no-nonsense LAPD detective - on this new show that is equal parts police procedural and Warner Bros cartoon.
Detective Tribeca works out of a precinct also populated with high-decibel Lt Chet Atkins (played by Jere Burns), silky-smooth Detective D.J. Tanner (Deon Cole), dashing Jay Geils (Hayes MacArthur) - who is Tribeca's partner and romantic squeeze - and Dr Scholls, the bookish-but-sexy blonde who serves as medical examiner (Andree Vermeulen).
Part of what makes the series successful is the cast's commitment to playing things straight - as straight as any conventional cop drama - while also staying true to the singular absurdity of the alternate world they inhabit.
"We really do function like an actual procedural," says Jones. "We tell the story without referring to the comedy, and let the comedy speak for itself."
The stories are tangled whodunnits, while the comedy speaks loud and clear in bursts that mine the trove of crime-show cliches. (When a cop says, "We turned the apartment upside down and we didn't find anything," the apartment has literally been turned upside down.)
This sort of hijinks differs markedly from Jones' previous comedies The Office and Parks and Recreation, with their looser, mockumentary style.
"This is highly staged, highly choreographed. You have to be on your mark," says Jones.
"A lot of our jokes are visual, and they require details and concentration from every department across the board - wardrobe, lighting, special effects, stunts, animal trainers, makeup, hair. Everybody's challenged every single week."
The Office star Steve Carell and his comedian wife, Nancy Walls Carell, created Angie Tribeca, and the show has as much fun mining the cliches of police procedural as they do exploring the tropes of moody/damaged police officers.
"We want to make something artful, but still keep the jokes dumb," Jones explains.
"That's a skill: to match the high-and-low. And we take the job very seriously."
When: Tuesday, 8.30pm
What: Cop comedy